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(11) | EP 1 008 833 B1 |
| (12) | EUROPEAN PATENT SPECIFICATION |
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Method and apparatus for determining fringe number in a fiber-optic gyro Verfahren und Vorrichtung zum Bestimmen der Interferenzstreifenordnung in einem faseroptischen Kreisel Méthode et dispositif pour déterminer l' ordre de frange dans un gyroscope à fibre optique |
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| Note: Within nine months from the publication of the mention of the grant of the European patent, any person may give notice to the European Patent Office of opposition to the European patent granted. Notice of opposition shall be filed in a written reasoned statement. It shall not be deemed to have been filed until the opposition fee has been paid. (Art. 99(1) European Patent Convention). |
BACKGROUND OF THE INVENTION
[0001] This invention relates generally to fiber-optic gyros and more specifically to the signal processing associated with fiber-optic gyros.
[0002] Fiber-optic gyros measure rate of rotation by determining the phase difference in light waves that propagate in opposite directions through a coil wound with optical fiber. Light waves that propagate through the coil in the direction of rotation take a longer time than light waves that propagate through the coil in the direction opposite to the direction of rotation. This difference in time, measured as the phase difference between counter-propagating light waves, is proportional to the angular velocity of the coil.
[0003] A typical block diagram for a fiber-optic gyro is shown in Fig. 1. A light source 2 supplies a reasonably coherent light beam to the optical-fiber interferometer 4 which causes the input light beam to be split into two light beams that are fed into opposite ends of an optical fiber configured as a coil. The light beams emerging from opposite ends of the optical fiber are recombined into a single output light beam that feeds into the detector 6.
[0004] The detected light intensity I (i.e. output of the detector 6) is given by
where Io is the peak detected light intensity and θ(t) is the phase difference between the two beams expressed as a function of time.
[0005] The phase difference θ(t) typically takes the form
where Φ(t) is the phase-modulation generating function and Φ(t)mod2π is the phase modulation introduced by a phase modulator within the interferometer 4, τ is the propagation time through the fiber optic coil, and (φS + 2πn) is the so-called Sagnac phase resulting from the rotation of the fiber-optic coil about its axis. The integer n (called the Sagnac fringe number or simply fringe number) is either positive or negative and the Sagnac residual phase φS is constrained to the range -π ≤ φS < π.
[0006] The output of the detector 6 is high-pass filtered to remove the DC component, then converted to digital form by the analog-to-digital converter 8, and finally processed in the digital processor 10 to yield at the output a measure of the rate and angle of rotation of the interferometer 4. In addition, the digital processor 10 generates a phase-modulation generating function Φ(t), the modulo-2π portion of which is converted to analog form by the digital-to-analog converter 12 and supplied to the phase modulator in the interferometer 4.
[0007] The phase-modulation generating function Φ(t) typically consists of a number of phase-modulation components among which are ΦSE(t) and ΦM(t). The phase- modulation component ΦSE(t) is typically a stepped waveform with steps that change in height by -φSE at τ intervals where φSE is an estimate of φS. Thus, the ΦSE(t) modulation cancels in large part φS. The accurate measurement of the uncancelled portion of the Sagnac residual phase φS is of great importance in that it is the quantity that is used in refining the estimate of the Sagnac phase and generating the ΦSE(t) phase-modulation component.
[0008] The accurate measurement of the uncancelled portion of the Sagnac residual phase is greatly facilitated by choosing the ΦM(t) phase-modulation component such that [ΦM(t)- ΦM(t-τ)] is equal to jφM where the permitted values of j are the values -1 and 1 and φM is a predetermined positive phase angle somewhere in the vicinity of π/2 radians where the slope of the cosine function is greatest. This effect can be achieved, for example, by having ΦM(t) be a square wave with amplitude π/2 and period 2τ.
[0009] While it might appear that the best choice for φM would be π/2 where the slope of the cosine function is greatest, it has been shown that values between π/2 and π provide better noise performance.
[0010] The ΦM(t) modulation can also be a stepped function wherein the phase increases or decreases at τ intervals by φM. Under these circumstances,
where k is an integer which maintains the ΦM(t) modulation between 0 and 2π.
[0012] The equation above is the ideal phase difference equation, where φS - φSE = 0. For fiber-optic closed-loop calculation, two control parameters are inserted into the phase difference equation with the following result:
The rebalance phase error ε is given by
and the phase modulator scale factor error δ/π is given by
where φX is the change in light phase caused by a phase modulation step intended to produce a change of X radians. Note that if φX were correct and equal to X, then δ would be equal to zero.
[0013] The parameters φSE and φX (for a particular X) are driven by control loops to force two demodulation signals to zero. The first demodulation signal DMOD1 is given by
and the second demodulation signal DMOD2 is given by
where Pkj is the probability of occurrence of each state, Dkj is the scale factor demodulation polarity, Ikj is the amplitude of the signal that results from the high-pass filtering of the output signal from detector 6 which may be a function of k and j, and l is the average of Ikj expressed in units of
sin φM.
[0014] The DC bias parameter l is driven by a third control loop to force a third demodulation signal to zero. The third demodulation signal DMOD3 is given by
[0015] Fiber optic gyros generally employ broadband light sources in order to avoid polarization cross-coupling effects as the light propagates through the fiber. As a result, however, coherence is lost as non-reciprocal phase shifts between the clockwise and counter-clockwise beams are introduced. This leads to the "fringe visibility effect" whereby the interference pattern between the two beams loses contrast as the difference in optical paths increases.
[0016] In an interferometric fiber-optic gyro (IFOG), a phase shift is generated between counter-propagating beams in proportion to the applied angular rate. The Sagnac scale factor relates the phase shift to the rate. A typical Sagnac scale factor for a gyro used in navigation is 3 to 20 µrad/(deg/hr). The phase shift between the two beams in an IFOG is used to estimate the angular rate (assuming a calibrated Sagnac scale factor). However, the interferometer operates on a modulo 2π basis. That is, φ+2nπ cannot be distinguished from φ if n is an integer. For a Sagnac scale factor of 3.5 µrad/(deg/hr), 2π radians corresponds to approximately 500 deg/s.
[0017] Usually, the IF0G is used in applications where the initial angular rate is close to zero and then builds up to larger values. As long as the phase shift is continuously tracked from turn-on, the total phase including multiples of 2π can be estimated to yield actual angular rate. However, in certain applications, the gyro can be powered up in the presence of significant angular rate that will cause the initial condition to be incorrect. For example, if a gyro is powered up at a time it is spinning at 500 deg/s, it will appear that the phase shift is close to zero and the measured rate will be estimated to be near zero.
[0018] Up to now there has been no means for establishing the initial multiple of 2π (i.e. the fringe number) that was captured. The fringe visibility effect, which causes errors in the measurement of gyro phase, provides such a means.
[0019] US-A-4 969 017 pertains to a device for the measurement, in a wide range, of a non-reciprocal phase shift generated in a ring interferometer, to a measuring method and, chiefly, to an optic fiber gyrometer. It also concerns a method of measurement, notably a method for the measurement of rotation speed. The disclosure concerns an improvement in a measuring device comprising a phase modulation device enabling the phase to be automatically locked to an interference fringe of the device. The improvement lies mainly in the fact that the light source emits, in the ring, several light frequencies so as to make it possible to remove uncertainty on the order (0, π, 2π, etc.) of the interference fringe on which the automatic control is achieved. The disclosure can be applied notably to the making of devices for the measurement of angular speeds. The disclosure can be aplied chiefly to the making of optic fiber gyrometers. This is an example of a completely different approach to determining fringe number and describes a fiber-optic gyro wherein the light source is frequency modulated thereby producing at least two light frequencies, the fringe number being determined essentially by driving the fiber-optic loop simultaneously with two or more different light frequencies. This approach does not involve the fringe visibility effect and is completely different from the approach described in the present application.
BRIEF SUMMARY OF THE INVENTION
[0020] The invention is a method and apparatus for determining the fringe number for a fiber-optic gyro. The fiber-optic gyro comprises a light source feeding an interferometer that in turn feeds a detector. The detector output signal is a function of the fringe number and a plurality of controllable parameters. The method comprises the steps of (1) determining the values of the controllable parameters and (2) extracting the fringe number from the detector output signal utilizing the values of the controllable parameters.
BRIEF DESCRIPTION OF THE DRAWINGS
DESCRIPTION OF THE INVENTION
[0022] The fringe visibility effect in an IFOG results from the loss of interferometer fringe contrast as the interferometer phase grows. For modulation values that are odd multiples π/2, the fringe visibility effect vanishes. However, with overmodulation, the fringe visibility effect does cause errors that must be corrected if the greatest possible measurement accuracy is to be achieved.
[0023] It can be shown that given a broadband source, equation (1) becomes (ignoring powers of θ-squared greater than one)
While this equation is an approximation, it holds relatively well for typical fiber-optic gyro sources whose line-widths are on the order of 1% of the wavelength.
[0024] With φM equal to an odd-integer multiple of π/2 radians, the fringe visibility error vanishes because cosθ equals zero. For other values of φM in a closed-loop fiber-optic gyro operating within the confines of a single fringe (-π ≤ φS < π) the effect manifests itself as a bias error that is rate-dependent and normally appears as a simple scale-factor miscalibration. However, for multiple fringe operation (n > 1), the effect manifests itself as a bias error which is a function of phase shift within a fringe. Multiple-fringe operation is especially important in gyros with large Sagnac scale factors, the Sagnac scale factor being the ratio of the Sagnac phase to the rotation rate of the fiber-optic gyro.
[0025] The error in the detected light intensity I from detector 6 resulting from fringe visibility can be calculated in the following way. Using equations (4) and (11), we can obtain the intensity error due to fringe visibility for a fiber-optic gyro operating with a modulation amplitude φM.
where we have dropped second-order terms. The quantity Qnkj is given by the expression
where
and
The symbol Qav denotes the average detected light intensity level shift in units of
sin φM of the output signal from detector 6 signal prior to the high-pass filtering.
[0026] In order to constrain [ΦM(t)]mod2π to the range from 0 to a value less than 2π, k must satisfy the following relationship:
where
Combining equations (5), (11) and (12), we obtain
[0027] The quantity (I - DC intensity) in equation (19) corresponds to the amplitude of the signal that results from the high-pass filtering of the output signal from detector 6. Denoting the quantity (I - DC intensity) by Inkj we obtain
where the light intensity Inkj is expressed in units of
sin φM. The quantity I denotes the average detected light-intensity level shift in units
sinφM that results from the analog-to-digital conversion process performed by analog-to-digital converter 8. It can be shown that if the gyro loops described by equations (8), (9), and (10) are satisfied, the total detected light intensity will be a function of the modulation point defined by j and k.
[0028] The fiber-optic gyro operates in states Z, A, B, C, D, and E which are identified by corresponding (k,j) values. It follows from equation (20):
where we have replaced Inkj in each equation by a symbol identifying the associated state.
[0029] The fiber-optic gyro operates in three zones defined as follows:
Zone 1: -φM ≤ φS ≤ φM
Zone 2: -π ≤ φS < -φM
Zone 3: φM < φS < π
[0030] With closed-loop random overmodulation, the gyro can be modulated to any one of four states within the zone of operation. In zone 1, the available states are A, B, C, and D. In zone 2, the available states are B, C, D, and E. In zone 3, the available states are Z, A, B, and C. The probability of occurrence of a given state depends on the actual phase shift of operation.
[0031] In a closed-loop IFOG mechanization three control loops operate continuously in order to maintain the gyro control points at the chosen values. The first control loop, in the absence of the fringe visibility effect, maintains a controllable phase φSE of the interferometer output light beam equal to the Sagnac residual phase. As a result, the controllable phase becomes an estimate of the Sagnac residual phase. The presence of the fringe visibility effect results in the estimate of the Sagnac residual phase being offset by ε from the Sagnac residual phase.
[0032] A second control loop, in the absence of the fringe visibility effect, maintains the light phase change commanded of the interferometer phase modulator equal to the phase change produced by the phase modulator. The presence of the fringe visibility effect results in the phase change produced by the phase modulator being greater than the phase change commanded by the factor (1+δ/π).
[0033] The third control loop, in the absence of the fringe visibility effect, maintains the average value of the high-pass filtered output signal from detector 6 at zero. The bias l
sinφM is a result of the offset introduced by the analog-to-digital converter 8.
[0034] Each of the control loops involves a demodulation process which results in a demodulation signal. There are three such demodulation signals: DMOD1 associated with the first control loop; DMOD2 associated with the second control loop; and DMOD3 associated with the third control loop. The control parameters ε, δ, and l are adjusted by the control loops to null out the demodulation signals DMOD1, DMOD2, and DMOD3 simultaneously. In the absence of the fringe visibility effect, the three control parameters ε, δ, and l are sufficient to null out the three demodulation signals because of the symmetry of the interferometer cosine fimction. However, due to the asymmetries introduced for all but the zeroth fringe by the fringe visibility effect, the three control parameters are not sufficient, in the presence of the fringe visibility effect, to simultaneously null out the signals in all four modulation states on higher fringes even though the statistical averages of DMOD1, DMOD2, and DMOD3 can still be driven to zero.
[0035] This effect can be used to determine the actual fringe number of operation. An additional demodulation signal DMOD4 is used to measure the left-over signals in the interferometer output and this value is processed to determine the fringe number.
[0036] The equations for four demodulation signals DMOD1, DMOD2, DMOD3, and DMOD4 are shown below for the three zones. The first three demodulation signals follow from equations (8), (9), and (10). The fourth demodulation signal DMOD4 provides the means for determining the fringe number n.
The symbols z, a, b, c, d, and e stand for the probabilities of occurrence of modulation states Z, A, B, C, D, and E respectively. The probabilities can be determined by counting the occurrences of each state over a period of time.
[0037] The fringe number n is determined in the following way. The zone number is determined from φSE, which is very nearly equal to φS. Given the zone number, one of the equation sets (22), (23), and (24) is selected. The quantities DMOD1, DMOD2, and DMOD3, which are maintained at zero by the control loops, are set equal to zero and the equations in which they appear are solved for ε(n), δ(n), and l(n) for a specified set of n values by using standard numerical inversion methods for systems of linear equations. Typically, the set of n values will be limited to a small number. For example, given a fiber-optic gyro with a Sagnac scale factor (i.e. ratio of the phase difference between the counter propagating light beams to the rotation rate of the fiber-optic gyro) of 3.5 µrad/(deg/hr) and a rate range of ±1000 deg/s, the possible fringe numbers are -2, -1, 0, 1, and 2. The value of DMOD4(n) is then computed using the values for ε(n), δ(n), and l(n), substituting in the appropriate DMOD4 equation in equation sets (22), (23), and (24) using the particular values defined in equation (21). The value of DMOD4 is measured and compared with computed values of DMOD4(n). The n value corresponding to the DMOD4(n) that is closest to the measured value of DMOD4 is determined to be the fringe number.
[0038] This procedure can also be used on a continuous basis for self-test purposes to make sure that the interferometer did not "jump" fringes as a result of an error or transient.
(a) determining the values of the controllable parameters;
(b) extracting the fringe number from the detector output signal utilizing the fringe visibility effect and the values of the controllable parameters, the detector output signal in the absence of the fringe visibility effect being proportional to (1+cos θ) where θ is the difference in phase of the two light beams, the fringe visibility effect being manifested by the cos θ term in the expression (1-cos θ) being multiplied by a power series in θ squared.
(a1) transforming the detector output signal into a plurality of demodulation signals;
(a2) determining the values of the controllable parameters for which each of the plurality of demodulation signals has a predetermined value.
(b1) transforming the detector output signal into a demodulation signal;
(b2) determining the measured value of the demodulation signal for the values of the controllable parameters.
(b1) transforming the detector output signal into a demodulation signal;
(b2) determining the calculated value of a mathematical representation of the demodulation signal for each of a plurality of trial fringe numbers using the values of the controllable parameters.
(b1) transforming the detector output signal into a demodulation signal;
(b2) determining the measured value of the demodulation signal for the values of the controllable parameters;
(b3) determining the calculated value of a mathematical representation of the demodulation signal for each of a plurality of trial fringe numbers using the values of the controllable parameters.
(b4) determining the fringe number by comparing the measured value of the demodulation signal with the calculated values of the mathematical representation of the demodulation signals.
(a1) determining the zone of operation;
(a2) causing each demodulation signal DMODp=ΣPkjCpkjFnkj to equal a predetermined value Ap, p taking on the values 1, 2, and 3, Pkj being the probability of occurrence of state (k, j), Cpkj being numerical coefficients, the summation being over the states associated with the zone in which the fiber-optic gyro is operating;
(a3) obtaining values of ε, δ, and l by solving the equations ΣPkjCpkjFnkj=Ap for p equal to 1, 2, and 3 utilizing measured values for Fnkj, the summation being over the states associated with the zone of operation.
(b1) determining the zone of operation;
(b2) obtaining a measured value for demodulation signal DMOD4=ΣPkjC4kjFnkj utilizing measured values for Fnkj, Pkj being the probability of occurrence of state (k, j), C4kj being numerical coefficients.
(b1) determining the zone of operation;
(b2) obtaining calculated values for demodulation signal DMOD4=ΣPkjC4kjFnkj for each of a plurality of trial values of n utilizing calculated values for Fnkj, Pkj being the probability of occurrence of state (k,j), C4kj being numerical coefficients.
(b1) determining the zone of operation;
(b2) obtaining a measured value for demodulation signal DMOD4=ΣPkjC4kjFnkj utilizing measured values for Fnkj, Pkj being the probability of occurrence of state (k, j), C4kj being numerical coefficients;
(b3) obtaining calculated values for demodulation signal DMOD4=ΣPkjC4kjFnkj for each of a plurality of trial values of n utilizing calculated values for Fnkj.
(b4) identifying the trial value of n associated with the calculated value of the demodulation signal DMOD4 that is closest to the measured value of the demodulation signal DMOD4, the identified trial value of n being the fringe number.
(a) a means for determining the values of the controllable parameters;
(b) a means for extracting the fringe number from the detector output signal utilizing the fringe visibility effect and the values of the controllable parameters, the detector output signal in the absence of the fringe visibility effect being proportional to (1+cos θ) where is the difference in phase of the two light beams, the fringe visibility effect being manifested by the cos θ tenn in the expression (1+cos θ) being multiplied by a power series in θ squared.
(a1) a plurality of demodulators that transform the detector output signal into a plurality of demodulation signals;
(a2) a plurality of control loops that force each of the plurality of demodulation signals to have a predetermined value by adjusting the values of the controllable parameters;
(a3) a processor that utilizes the predetermined values of the plurality of demodulation signals to obtain values for the controllable parameters.
(b1) a demodulator that transforms the detector output signal into a demodulation signal;
(b2) a memory wherein the measured value of the demodulation signal is stored.
(b1) a demodulator that transforms the detector output signal into a demodulation signal;
(b2) a processor that determines the calculated values of a mathematical representation of the demodulation signal for each of a plurality of trial fringe numbers using the values of the controllable parameters.
(b1) a demodulator that transforms the detector output signal into a demodulation signal;
(b2) a memory wherein the measured value of the demodulation signal is stored;
(b3) a processor that determines the calculated values of a mathematical representation of the demodulation signal for each of a plurality of trial fringe numbers using the values of the controllable parameters.
(b4) a processor that equates the fringe number to the trial fringe number associated with the calculated value of the mathematical representation of the demodulation signal that is closest to the measured value of the demodulation signal.
(a1) a plurality of demodulators that transform the detector output signal into a plurality of demodulation signals DMODp,p taking on the values 1, 2, and 3;
(a2) a plurality of control loops that force each of the plurality of demodulation signals DMODp to have a predetermined value Ap by adjusting the values of the controllable parameters.
(a1) a processor that determines the zone of operation;
(a2) a processor that obtains values of ε, δ, and l by solving the equations ΣPkjCpkjFnkj = Ap for p equal to 1, 2, and 3 utilizing measured values for Fnkj, the quantities Ap being predetermined constants, Pkj being the probability of occurrence of state (k, j), Cpkj being numerical coefficients, the summation being over the states associated with the zone in which the fiber-optic gyro is operating.
(b1) a demodulator that transforms the detector output signal into a demodulation signal DMOD4;
(b2) a memory wherein the measured value of DMOD4 is stored.
(b1) a processor that determines the zone of operation;
(b2) a processor that obtains calculated values for demodulation signal DMOD4=ΣPkjC4kjFnkj for each of a plurality of trial values of n utilizing calculated values for Fnkj, Pkj being the probability of occurrence of state (k,j), C4kj being numerical coefficients.
(b1) a demodulator that transforms the detector output signal into a demodulation signal DMOD4;
(b2) a memory wherein the measured value of DMOD4 is stored;
(b3) a processor that determines the zone of operation;
(b4) a processor that obtains calculated values for demodulation signal DMOD4=ΣPkC4kjFnkj for each of a plurality of trial values of n utilizing calculated values for Fnkj, Pkj being the probability of occurrence of state (k, j), C4kj being numerical coefficients.
(a) Bestimmen der Werte der steuerbaren Parameter;
(b) Herausziehen oder Extrahieren der Streifen- oder Fringe-Zahl aus dem Detektorausgabesignal unter Verwendung des Streifensichtbarkeitseffekts und der Werte der steuerbaren Parameter, wobei das Detektorausgangssignal bei Abwesenheit des Streifensichtbarkeitseffekts proportional ist zu (1+cos θ), wobei θ die Phasendifferenz der zwei Lichtstrahlen ist, wobei der Streifensichtbarkeitseffekt manifestiert ist durch den cos θ-Term in dem Ausdruck (1+cos θ) multipliziert mit einer Potenzreihe von θ im Quadrat.
(a1) Umwandeln des Detektorausgangssignals in eine Vielzahl von Demodulationssignalen;
(a2) Bestimmen der steuerbaren Parameter, für die jede der Vielzahl von Demodulationssignalen einen vorbestimmten Wert besitzt.
(b1) Umwandeln des Detektorausgangssignals in ein Demodulationssignal;
(b2) Bestimmen des gemessenen Werts des Demodulationssignals für die Werte der steuerbaren Parameter.
(b1) Umwandeln des Detektorausgangssignals in ein Demodulationssignal;
(b2) Bestimmen des berechneten Werts einer mathematischen Darstellung des Demodulationssignals für jede einer Vielzahl von Versuchs-Streifenzahlen unter Verwendung der Werte der steuerbaren Parameter.
(b1) Umwandeln des Detektorausgangssignals in ein Demodulationssignal;
(b2) Bestimmen des gemessenen Werts des Demodulationssignals für die Werte der steuerbaren Parameter;
(b3) Bestimmen des berechneten Werts einer mathematischen Darstellung des Demodulationssignals für jede aus einer Vielzahl von Versuchs-Streifenzahlen unter Verwendung der Werte der steuerbaren Parameter.
(b4) Bestimmen der Streifen- oder Fringe-Zahl durch Vergleichen des gemessenen Werts des Demodulationssignals mit den berechneten Werten der mathematischen Darstellung des Demodulationssignals.
(a1) Bestimmen des Betriebsbereichs;
(a2) Bewirken, dass jedes Demodulationssignal DMODp = ΣPkjCpkjFnkj gleich einem vorbestimmten Wert Ap ist, wobei p die Werte 1, 2 und 3 annimmt, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, wobei Cpkj numerische Koeffizienten sind, wobei die Summierung über die Zustände hinweg erfolgt, die mit dem Bereich assoziiert sind, in dem der faseroptische Kreisel arbeitet;
(a3) Erhalten von Werten für ε, δ und ℓ durch Lösen der Gleichungen ΣPkjCpkjFnkj = Ap für p gleich 1, 2 und 3, unter Verwendung gemessener Werte für Fnkj, wobei die Summierung über die Zustände erfolgt, die mit dem Betriebsbereich assoziiert sind.
(b1) Bestimmen des Betriebsbereichs;
(b2) Erhalten eines gemessenen Werts für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj unter Verwendung gemessener Werte für Fnkj, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, und wobei C4kj numerische Koeffizienten sind.
(b1) Bestimmen des Betriebsbereichs;
(b2) Erhalten berechneter Werte für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj für jeden einer Vielzahl von Versuchswerten für n unter Verwendung berechneter Werte für Fnkj, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, und wobei C4kj numerische Koeffizienten sind.
(b1) Bestimmen des Betriebsbereichs;
(b2) Erhalten eines gemessenen Werts für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj unter Verwendung gemessener Werte für Fnkj, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, und wobei C4kj numerische Koeffizienten sind;
(b3) Erhalten berechneter Werte für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj für jeden einer Vielzahl von Versuchswerten für n unter Verwendung berechneter Werte für Fnkj.
(b4) Identifizieren des Versuchswerts von n, welcher mit dem berechneten Wert des Demodulationssignals DMOD4 assoziiert ist, welcher am nächsten zu dem gemessenen Wert des Demodulationssignals DMOD4 ist, wobei der identifizierte Versuchswert von n die Streifen- oder Fringe-Zahl ist.
(a) Mittel zum Bestimmen der Werte der steuerbaren Parameter;
(b) Mittel zum Herausziehen oder Extrahieren der Streifen- oder Fringe-Zahl aus dem Detektorausgabesignal unter Verwendung des Streifensichtbarkeitseffekts und der Werte der steuerbaren Parameter, wobei das Detektorausgangssignal bei Abwesenheit des Streifensichtbarkeitseffekts proportional ist zu (1+cos θ), wobei θ die Phasendifferenz der zwei Lichtstrahlen ist, wobei der Streifensichtbarkeitseffekt manifestiert ist durch den cos θ-Term in dem Ausdruck (1+cos θ) multipliziert mit einer Potenzreihe von θ im Quadrat.
(a1) eine Vielzahl von Demodulatoren, die das Detektorausgangssignal in eine Vielzahl von Demodulationssignalen umwandeln;
(a2) eine Vielzahl von Steuerschleifen, die erzwingen, dass jedes der Vielzahl von Demodulationssignalen einen vorbestimmten Wert besitzt, und zwar durch Anpassen oder Einstellen der Werte der steuerbaren Parameter;
(a3) einen Prozessor, der die vorbestimmten Werte der Vielzahl von Demodulationssignalen verwendet, um Werte für die steuerbaren Parameter zu erhalten.
(b1) einen Demodulator, der das Detektorausgangssignal in ein Demodulationssignal umwandelt;
(b2) einen Speicher, in dem der gemessene Wert des Demodulationssignals gespeichert wird.
(b1) einen Demodulator, der das Detektorausgangssignal in ein Demodulationssignal umwandelt;
(b2) einen Prozessor, der die berechneten Werte einer mathematischen Darstellung des Demodulationssignals für jede einer Vielzahl von Versuchs-Streifenzahlen bestimmt unter Verwendung der Werte der steuerbaren Parameter.
(b1) einen Demodulator, der das Detektorausgangssignal in ein Demodulationssignal umwandelt;
(b2) einen Speicher, in dem der gemessene Wert des Demodulationssignals gespeichert wird;
(b3) einen Prozessor, der die berechneten Werte einer mathematischen Darstellung des Demodulationssignals für jede einer Anzahl von Versuchs-Streifenzahlen bestimmt unter Verwendung der Werte der steuerbaren Parameter.
(b4) einen Prozessor, der die Streifen- oder Fringe-Zahl mit der Versuchs-Streifenzahl gleichsetzt, die mit dem berechneten Wert der mathematischen Darstellung des Demodulationssignals assoziiert ist, welcher dem gemessenen Wert des Demodulationssignals am nächsten kommt.
(a1) eine Vielzahl von Demodulatoren, die das Detektorausgangssignal in eine Vielzahl von Demodulationssignalen DMODp umwandeln, wobei p die Werte 1, 2 und 3 annimmt;
(a2) eine Vielzahl von Steuerschleifen, die erzwingen, dass jede der Vielzahl von Demodulationssignalen DMODp einen vorbestimmten Wert Ap besitzt, und zwar durch Einstellen bzw. Anpassen der Werte der steuerbaren Parameter.
(a1) einen Prozessor, der den Betriebsbereich bestimmt;
(a2) einen Prozessor, der Werte für ε, δ und ℓ erhält durch Lösen der Gleichungen ΣPkjCpkjFnkj = Ap für p gleich 1, 2 und 3 unter Verwendung gemessener Werte für Fnkj, wobei die Größen Ap vorbestimmte Konstanten sind, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, wobei Cpkj numerische Koeffizienten sind und wobei die Summierung über die Zustände erfolgt, die mit dem Bereich assoziiert sind, in dem der faseroptische Kreisel arbeitet.
(b1) einen Demodulator, der das Detektorausgangssignal in ein Demodulationssignal DMOD4 umwandelt;
(b2) einen Speicher, in dem der gemessene Wert von DMOD4 gespeichert wird.
(b1) einen Prozessor, der den Betriebsbereich bestimmt;
(b2) einen Prozessor, der berechnete Werte für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj für jede einer Vielzahl von Versuchswerten von n erhält unter Verwendung berechneter Werte für Fnkj, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, und wobei C4kj numerische Koeffizienten sind.
(b1) einen Demodulator, der das Detektorausgangssignal in ein Demodulationssignal DMOD4 umwandelt;
(b2) einen Speicher, in dem der gemessene Wert von DMOD4 gespeichert wird;
(b3) einen Prozessor, der den Betriebsbereich bestimmt;
(b4) einen Prozessor, der berechnete Werte für das Demodulationssignal DMOD4 = ΣPkjC4kjFnkj für jede einer Vielzahl von Versuchswerten von n erhält unter Verwendung berechneter Werte für Fnkj, wobei Pkj die Wahrscheinlichkeit des Auftretens des Zustands (k, j) ist, und wobei C4kj numerische Koeffizienten sind.
(b5) einen Prozessor, der den Versuchswert von n identifiziert, welcher mit dem berechneten Wert des Demodulatonssignals DMOD4 assoziiert ist, der dem gemessenen Wert des Demodulationssignals DMOD4 am nächsten kommt, wobei der identifizierte Versuchswert von n die Streifen- oder Fringe-Zahl ist.
(a) déterminer les valeurs des paramètres contrôlables ;
(b) extraire l'ordre de frange du signal de sortie du détecteur en utilisant l'effet de visibilité de franges et les valeurs des paramètres contrôlables, le signal de sortie du détecteur en l'absence d'effet de visibilité de franges étant proportionnel à (1+cosθ), où θ est la différence de phase des deux faisceaux lumineux, l'effet de visibilité de franges se manifestant par le terme cosθ dans l'expression (1-cosθ) multipliée par une succession de puissances de θ au carré.
(a1) transformer le signal de sortie du détecteur en une pluralité de signaux de démodulation ; et
(a2) déterminer les valeurs des paramètres contrôlables pour lesquelles chacun de la pluralité de signaux de démodulation a une valeur prédéterminée.
(b1) transformer le signal de sortie du détecteur en un signal de démodulation ;
(b2) déterminer la valeur mesurée du signal de démodulation pour les valeurs des paramètres contrôlables.
(b1) transformer le signal de sortie du détecteur en un signal de démodulation ;
(b2) déterminer la valeur calculée d'une représentation mathématique du signal de démodulation pour chacun d'une pluralité d'ordres de frange d'essai en utilisant les valeurs des paramètres contrôlables.
(b1) transformer le signal de sortie du détecteur en un signal de démodulation ;
(b2) déterminer la valeur mesurée du signal de démodulation pour les valeurs des paramètres contrôlables ;
(b3) déterminer la valeur calculée d'une représentation mathématique du signal de démodulation pour chacun d'une pluralité d'ordres de frange d'essai en utilisant les valeurs des paramètres contrôlables.
(b4) déterminer l'ordre de frange en comparant la valeur mesurée du signal de démodulation aux valeurs calculées de la représentation mathématique du signal de démodulation.
(a1) déterminer la zone de fonctionnement ;
(a2) amener chaque signal de démodulation DMODp = ΣPkjCpkjFnkj à être égal à une valeur prédéterminée Ap, p prenant les valeurs 1, 2 et 3, Pkj étant la probabilité de survenance de l'état (k,j), Cpkj étant des coefficients numériques, la sommation se faisant sur les états associés à la zone dans laquelle le gyroscope à fibres optiques fonctionne ;
(a3) obtenir des valeurs de ε, δ et l en résolvant les équations ΣPkjCpkjFnkj = Ap pour p égale 1, 2, et 3 en utilisant les valeurs mesurées de Fnkj, la sommation se faisant sur les états associés à la zone de fonctionnement.
(b1) déterminer la zone de fonctionnement ;
(b2) obtenir une valeur mesurée du signal de démodulation DMOD4 = ΣPkjC4kjFnkj, en utilisant des valeurs mesurées de Fnkj, Pkj étant la probabilité de survenance de l'état (k,j), C4kj étant des coefficients numériques.
(b1) déterminer la zone de fonctionnement ;
(b2) obtenir des valeurs calculées pour le signal de démodulation DMOD4 = ΣPkjC4kjFnkj pour chacune d'une pluralité de valeurs d'essai de n en utilisant des valeurs calculées de Fnkj, Pkj étant la probabilité de survenance de l'état (k,j), C4kj étant des coefficients numériques.
(b1) déterminer la zone de fonctionnement ;
(b2) obtenir une valeur mesurée d'un signal de démodulation DMOD4 = ΣPkjC4kjFnkj en utilisant les valeurs mesurées de Fnkj, Pkj étant la probabilité de survenance de l'état (k,j), C4kj étant des coefficients numériques ;
(b3) obtenir des valeurs calculées pour le signal de démodulation DMOD4 = ΣPkjC4kjFnkj pour chacune de plusieurs valeurs d'essai de n en utilisant des valeurs calculées pour Fnkj.
(b4) identifier la valeur d'essai de n associée à la valeur calculée du signal de démodulation DMOD4, qui est la plus proche de la valeur mesurée du signal de démodulation DMOD4, la valeur d'essai identifiée de n étant l'ordre de frange.
(a) un moyen pour déterminer les valeurs des paramètres contrôlables ;
(b) un moyen pour extraire l'ordre de frange du signal de sortie du détecteur en utilisant l'effet de visibilité de franges et les valeurs des paramètres contrôlables, le signal de sortie du détecteur en l'absence d'effet de visibilité de franges étant proportionnel à (1+cosθ), où θ est la différence de phase des deux faisceaux lumineux, l'effet de visibilité de franges se manifestant par le terme cosθ dans l'expression (1-cosθ) multipliée par une succession de puissances de θ au carré.
(a1) une pluralité de démodulateurs qui transforment le signal de sortie du détecteur en une pluralité de signaux de démodulation ;
(a2) une pluralité de boucles de commande qui forcent chacun de la pluralité de signaux de démodulation à avoir une valeur prédéterminée en réglant les valeurs des paramètres contrôlables ;
(a3) un processeur qui utilise les valeurs prédéterminées de la pluralité de signaux de démodulation pour obtenir des valeurs des paramètres contrôlables.
(b1) un démodulateur qui transforme le signal de sortie du détecteur en un signal de démodulation ;
(b2) une mémoire dans laquelle la valeur mesurée du signal de démodulation est stockée.
(b1) un démodulateur qui transforme le signal de sortie du détecteur en un signal de démodulation ;
(b2) un processeur qui détermine les valeurs calculées d'une représentation mathématique du signal de démodulation pour chacun d'une pluralité d'ordres de frange d'essai en utilisant les valeurs des paramètres contrôlables.
(b1) un démodulateur qui transforme le signal de sortie du détecteur en un signal de démodulation ;
(b2) une mémoire dans laquelle la valeur mesurée du signal de démodulation est stockée ;
(b3) un processeur qui détermine les valeurs calculées d'une représentation mathématique du signal de démodulation pour chacun d'une pluralité d'ordres de frange d'essai en utilisant les valeurs des paramètres contrôlables.
(b4) un processeur qui rend l'ordre de frange égal à un ordre de frange d'essai associé à la valeur calculée de la représentation mathématique du signal de démodulation qui est la plus proche de la valeur mesurée du signal de démodulation.
(a1) une pluralité de démodulateurs qui transforment le signal de sortie du détecteur en une pluralité de signaux de démodulation DMODp, p prenant les valeurs 1, 2 et 3,
(a2) une pluralité de boucles de commande qui forcent chacun de la pluralité de signaux de démodulation DMODp à avoir une valeur prédéterminée Ap, en réglant les valeurs des paramètres contrôlables.
(a1) un processeur qui détermine la zone de fonctionnement ;
(a2) un processeur qui fournit des valeurs de ε, δ et l en résolvant les équations ΣPkjCpkjFnkj = Ap pour p égale 1, 2, et 3 en utilisant les valeurs mesurées de Fnkj, les quantités Ap étant des constantes prédéterminées, Pkj étant la probabilité de survenance de l'état (k,j), Cpkj étant des coefficients numériques, la sommation se faisant sur les états associés à la zone dans laquelle le gyroscope à fibres optiques fonctionne.
(b1) un démodulateur qui transforme le signal de sortie du détecteur en un signal de démodulation DMOD4 ;
(b2) une mémoire dans laquelle la valeur mesurée de DMOD4 est stockée.
(b1) un processeur qui détermine la zone de fonctionnement ;
(b2) un processeur qui fournit des valeurs calculées pour le signal de démodulation DMOD4 = ΣPkjC4kjFnkj pour chacune d'une pluralité de valeurs d'essai de n en utilisant des valeurs calculées de Fnkj, Pkj étant la probabilité de survenance de l'état (k,j), C4kj étant des coefficients numériques.
(b1) un démodulateur qui transforme le signal de sortie du détecteur en un signal de démodulation DMOD4 ;
(b2) une mémoire dans laquelle la valeur mesurée de DMOD4 est stockée.
(b3) un processeur qui détermine la zone de fonctionnement ;
(b4) un processeur qui fournit des valeurs calculées pour le signal de démodulation DMOD4 = ΣPkjC4kjFnkj pour chacune d'une pluralité de valeurs d'essai de n en utilisant des valeurs calculées de Fnkj, Pkj étant la probabilité de survenance de l'état (k,j), C4kj étant des coefficients numériques.
(b5) un processeur qui identifie la valeur d'essai de n associée à la valeur calculée du signal de démodulation DMOD4, qui est la plus proche de la valeur mesurée du signal de démodulation DMOD4, la valeur d'essai identifiée de n étant l'ordre de frange.